10 The straight line \(l\) has equation \(\mathbf { r } = 2 \mathbf { i } - \mathbf { j } - 4 \mathbf { k } + \lambda ( \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } )\). The plane \(p\) has equation \(3 x - y + 2 z = 9\). The line \(l\) intersects the plane \(p\) at the point \(A\).
- Find the position vector of \(A\).
- Find the acute angle between \(l\) and \(p\).
- Find an equation for the plane which contains \(l\) and is perpendicular to \(p\), giving your answer in the form \(a x + b y + c z = d\).